With ID and User ad dimensions, I added the following expression to represent the min timestamp. Without definining an else clause, the non min values would be missing and with the presentation tab -> suppress missing checkbox enabled you should lose the unwanted (non-min values).
min( total <ID> Timestamp ), only(Timestamp))
ps: i noticed your example showed min values over ID and not the combination of ID and User. if you need a more complicated example just let me know.